The Signs in John's Gospel

At the end of his gospel John tells us the reason why he wrote his gospel and why he based it around the miraculous signs performed by the Lord Jesus.

Jesus did many other miraculous signs in the presence of his disciples, which are not recorded in this book. But these are written that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name. (John 20:30-31)

If the signs occupy such a central role, then we need to appreciate what they signified. To do that we need to understand the effect they had upon the people who witnessed them, the Jewish Nation. How did they react to these miraculous signs? What did they say about them? What did they understand by them? And what did they do about them?